The department of Mathematics has organized a two day invited lecture series by Dr. S. Kumaresan, a celebrated mathemeticial and pedagogue in India. The lecture series took place on 9-10 March 2026 at the Seminar Hall, Department of Mathematics, RKMVERI Belur Campus.
Abstract:
Understanding the structure of linear operators on finite-dimensional vector spaces is a central objective of linear algebra. This lecture series discusses the decomposition of vector spaces relative to a linear operator and the resulting canonical representations. Beginning with the concepts of invariant subspaces and direct sum decompositions, the lectures examine how polynomial expressions in a linear operator generate invariant subspaces through kernels of operators of the form $p(A)$. These ideas lead naturally to the study of eigenvalues, diagonalizable operators, nilpotent transformations, and generalized eigenvectors. Using these tools, the structural properties of linear maps are developed, culminating in canonical representations such as the Jordan canonical form. The lecture series highlights how these decompositions reveal the intrinsic algebraic structure of linear operators and provide a systematic framework for simplifying their matrix representations.
About the speaker:
Dr. S. Kumaresan is a distinguished mathematician and pedagogue, and former Dean of the School of Mathematics and Statistics at the University of Hyderabad. An alumnus of the Tata Institute of Fundamental Research (TIFR) and a former visiting member of the Institute for Advanced Study, Princeton, he is most celebrated as the founder and former director of the Mathematics Training and Talent Search (MTTS) Programme. Since 1993, he has revolutionized Indian mathematics education by promoting a discovery-based pedagogy over rote learning. A recipient of the prestigious INSA Teachers Award, Dr. Kumaresan is also a prolific author of foundational textbooks, including Linear Algebra: A Geometric Approach and Topology of Metric Spaces, which remain essential resources for students across India.
Link of the paper: https://4dspace.mtts.org.in/expository-article-download.php?ai=174
| Faculty/Staff Name | Details |
|---|---|
| Brahmachari Tamal (Primary Coordinator) | Mathematics – Belur Campus |
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